# Pascals Triangle: 100% of the Numbers Are Even!

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Australian Mathematics Teacher, v66 n1 p25-28 2010

Pascal's triangle is an arrangement of the binomial coefficients in a triangle. Each number inside Pascal's triangle is calculated by adding the two numbers above it. When all the odd integers in Pascal's triangle are highlighted (black) and the remaining evens are left blank (white), one of many patterns in Pascal's triangle is displayed. By comparing the pattern of black cells (odd integers) to the shaded parts of the fractal called the Sierpinski triangle, the authors were guided to the conjecture that as the number of rows of Pascal's triangle increases, so too does the percentage of even numbers, i.e., the further down one looks, the whiter the pattern seems to get. The authors decided to consider the triangle as a number of stages, where each stage finishes at a row of odd numbers. From this, they calculated the percentage of even numbers in each stage up to the third. In this article, the authors set out to find what percentage of integers would be even in the nth Stage and conclude that 100% of the numbers are even, (although they are not)! (Contains 2 figures and 2 tables.)

Descriptors: Mathematics Activities, Numbers, Geometric Concepts, Mathematics Instruction, Teaching Methods, Mathematical Formulas, Computation

Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office[at]aamt.edu.au; Web site: http://www.aamt.edu.au

Author: **Bhindi, Nayan; McMenamin, Justin**

Source: https://eric.ed.gov/?q=a&ft=on&ff1=dtySince_1992&pg=3691&id=EJ885906